SOLUTION: Find the sum of those numbers between 1000 and 6000 every one of whose digits is one of the numbers 0, 2, 5 or 7. Give your answer as a product of prime numbers.

Question 580641: Find the sum of those numbers between 1000 and 6000 every one of whose digits is one of the numbers 0, 2, 5 or 7. Give your answer as a product of prime numbers.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The first digit cannot be 0 or 7, so the only options are 2 and 5. There will be two sets of numbers, those in the 2000's and those in the 5000's, and there will be the same number with a 2 in the thousands place as with a 5 in the thousands place. The average value of the thousands place digit is 3.5.
There are 4 choices for each of the other 3 digits, making possible combinations, from 000 to 777, and all choices are equally likely so the average value for each digit is .
The total number of 4 digit numbers meeting the requirement is .
The sum of all those numbers is 1000 times the sum of the thousands digits, plus 100 times the sum of the hundreds digits, plus 10 times the sum of the tens digits, plus the sum of the ones digits.
Those sums will be the average for the position (3.5 for all positions) times the number of digits in that position added (128 in each case).
So the sum of all 128 numbers is

RELATED QUESTIONS
Find the number of 7 digit numbers the sum of whose digits is even? (answered by nyc_function)

find two numbers. the sum of the digits is 20 and one of the numbers is 4 times the... (answered by muffin8)

1. The sum of 4 integers is 24 and their product is 945. What are those integers? 2.... (answered by CPhill,greenestamps)

What is the smallest square number that is the sum of two square numbers. Find two square (answered by MathLover1)

Solve each system using substitution ------------------------------------ 1.the sum of... (answered by mickclns)

Unisng nonzero whole numbers there is just one combination of two numbers whose sum is 2... (answered by Edwin McCravy)

find two positive numbers whose sum is 324 and the sum of those squares is a... (answered by Fombitz)

one number is twice a second number. the sum of those numbers is 45. find the... (answered by macston)

Your task is to find two different numbers that sum to 1000. One number must be a... (answered by TutorDelphia)